1. INC 112 Basic Circuit Analysis Week 5 Thevenin’s Theorem

2. Special Techniques Superposition Theorem Thevenin’s Theorem Norton’s Theorem Source Transformation

3. Linearity Characteristic If R L change its value, how will it effect the current and voltage across it?

4. I V V OC I SC For any circuit constructed from only linear components Not just RL, all resistors have this property. Voc = Voltage open-circuit Isc = Current short-circuit

5. Thevenin’s Theorem When we are interested in current and voltage across RL, we can simplify other parts in the circuit. Equivalent circuit

6. I V V OC I SC Voc = Voltage open-circuit Isc = Current short-circuit R = R equivalent Slope = 1/R

7. Thevenin’s Equivalent Circuit Thevenin’s equivalent circuit VTH = Voc (by removing RL and find the voltage difference between 2 pins) RTH (by looking into the opened connections that we remove RL, see how much resistance from the connections. If we see a voltage source, we short circuit. If we see a current source, we open circuit.)

8. Why do we need equivalent circuit? To analyze a circuit with several values of RL For circuit simplification (source transformation) To find RL that gives maximum power (maximum power transfer theorem)

9. Procedure 1. Remove RL from the circuit 2. Find voltage difference of the 2 opened connections. Let it equal VTH. 3.From step 2 find RTH by 3.1 short-circuit voltage sources 3.2 open-circuit current sources 3.3 Look into the 2 opened connections. Find equivalent resistance.

10. Example Find Thevenin’s equivalent circuit and find the current that passes through RL when RL = 1Ω

11. 0V 10V 0V 6V Find VTH

12. Short voltage source RTH Find RTH

13. Thevenin’s equivalent circuit If RL = 1Ω, the current is

14. Example Find Thevenin’s equivalent circuit

15. Find VTH 0V 5V 0V 3V

16. Open circuit current source RTH Find RTH

17. Thevenin’s equivalent circuit

18. Example: Bridge circuit Find Thevenin’s equivalent circuit

19. Find VTH 0V 10V 8V 2V VTH = 8-2 = 6V

20. Find RTH RTH

22. Thevenin’s equivalent circuit

23. Special Techniques Superposition Theorem Thevenin’s Theorem Norton’s Theorem Source Transformation

24. I V V OC I SC For any point in linear circuit

25. Thevenin’s Equivalent Circuit

26. Norton’s Equivalent Circuit In= Isc from replacing RL with an electric wire (resistance = 0) and find the current Rn = RTH (by looking into the opened connections that we remove RL, see how much resistance from the connections. If we see a voltage source, we short circuit. If we see a current source, we open circuit.)

27. Example Find Norton’s equivalent circuit and find the current that passes through RL when RL = 1Ω

28. Find In Find R total Find I total Current divider

29. Short voltage source RTH Find Rn

30. Norton’s equivalent circuit If RL = 1Ω, the current is

31. Relationship Between Thevenin’s and Norton’s Circuit I V V OC I SC Slope = - 1/Rth

32. Norton’s equivalent circuit Thevenin’s equivalent circuit Same R value

33. Example Find Norton’s equivalent circuit

34. Find In Current divider

35. Open circuit current source RTH Find RTH

36. Norton’s equivalent circuit

37. Thevenin’s equivalent circuit Norton’s equivalent circuit 0.2 x 15 = 3

38. Equivalent Circuits with Dependent Sources We cannot find Rth in circuits with dependent sources using the total resistance method. But we can use

39. Example Find Thevenin and Norton’s equivalent circuit

40. Find Voc I1 I2 KVL loop1 KVL loop2

41. I1 I2 Solve equations I1 = 3.697mAI2 = 3.678mA

42. Find Isc I1 I2 I3 KVL loop1 KVL loop2 KVL loop3

43. Find Isc I1 I2 I3 I1 = 0.632mA I2 = 0.421mA I3 = -1.052 A Isc = I3 = -1.052 A

44. Thevenin’s equivalent circuit Norton’s equivalent circuit